Seminar: Up to Six Loops, with help from Steinmann

As observed by Steinmann in the early 60's, functions appearing in scattering amplitudes not only have physical branch cuts, but also obey conditions on their double discontinuities, known as Steinmann relations. We have found these Steinmann relations to be particularly powerful in the context of the six-particle amplitude in planar N=4 super Yang-Mills. There, my collaborators and I build ansatze of "Steinmann Hexagon Functions" and then constrain them using a small list of physical conditions. We also obtain additional constraints based on Cosmic Galois Theory, a mathematical conjecture that constrains the constants which appear in scattering amplitudes. Using these methods we compute the complete amplitude through six loops with no need to draw Feynman diagrams or perform Feynman integrals.